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International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 1, Pages 1-13
http://dx.doi.org/10.1155/S0161171284000016

The regularity series of a Cauchy space

Department of Pure and Applied Mathematics, Washington State University, Pullman 99164-2930, Washington, USA

Received 16 December 1983

Copyright © 1984 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This study extends the notion of regularity series from convergence spaces to Cauchy spaces, and includes an investigation of related topics such as that T2 and T3 modifications of a Cauchy space and their behavior relative to certain types of quotient maps. These concepts are applied to obtain a new characterization of Cauchy spaces which have T3 completions.